Peaucellier–Lipkin linkage

Peaucellier-Lipkin Inversor

PeaucellierApparatus

The Peaucellier-Lipkin linkage with a rocker-slider four-bar as its driver

Peaucellier–Lipkin linkage is a mechanical linkage invented in the 19th century that converts linear motion to circular motion, and vice versa, without any sliding parts. It is the first known linkage capable of transforming a rotary motion into a perfect straight line, and it marked a significant advancement in the development of geometric mechanisms. The invention of the Peaucellier–Lipkin linkage is attributed to two engineers, Charles-Nicolas Peaucellier (1832–1913) from France and Yom Tov Lipman Lipkin (1846–1876) from Russia.

History

The Peaucellier–Lipkin linkage was discovered independently by both Peaucellier and Lipkin in the late 1860s. Peaucellier, a French army officer, was the first to publish his discovery in 1864, while Lipkin, a Russian mathematician, came up with the design around the same time but published his work later. The invention was a significant breakthrough in kinematics, the branch of mechanics that deals with motion without considering the forces that cause it.

Description

The Peaucellier–Lipkin linkage consists of several rods connected in a rhombus shape, with one additional rod connecting one corner of the rhombus to a fixed point. The lengths of the rods and their connection points are designed so that as the linkage moves, one point of the rhombus traces a straight line. This mechanism is known as an inversor because it can invert the position of a point within a circle to a corresponding point outside the circle, maintaining the property that the product of the distances to the two points is constant.

Mechanism

The key to the Peaucellier–Lipkin linkage's ability to generate a straight-line motion lies in its geometric properties. The linkage is composed of seven rods: one fixed-length coupler rod, four rods of equal length forming a rhombus, and two rods of equal length connecting opposite vertices of the rhombus to a fixed pivot point. The lengths of the rods are chosen such that the coupler point, which is attached to one vertex of the rhombus, moves in a perfect straight line as the linkage goes through its motion.

Applications

Although the Peaucellier–Lipkin linkage is primarily of historical and theoretical interest, it has been used in various engineering applications where precise straight-line motion is required. Before the advent of modern digital control systems, it was used in steam engines, pumps, and other machinery to convert rotary motion into linear motion. Today, it serves as an educational tool in mechanical engineering and physics to demonstrate principles of kinematics and mechanical design.

See Also

• Linkage (mechanical)
• Kinematics
• Four-bar linkage
• Straight-line mechanism